homework and exercises - Unintuitive: Aim the barrel downward to compensate for the uphill?

I came across the following physics exercise:

A high-powered 7-mm Remington magnum rifle fires a bullet with a velocity of $900$ m/s on a rifle range. Neglect air resistance.
(a) Calculate the distance $h$ such a bullet will drop at a range of $200$ m when fired horizontally.
(b) To compensate for the drop of the bullet, when the telescope sight is pointed right at the target, the barrel of the gun is aligned to be slanted slightly upward, pointed a distance $h$ above the target. The downward fall due to gravity then makes the bullet strike the target as desired. Suppose, however, such a rifle is fired uphill at a target $200$ m distance. If the upward slope of the hill is $45^\circ$, should you aim above or below the target, and by how much? What should you do when shooting on a downhill slope at $45^\circ$ below horizontal?

Part (a) was easy as $\pi$. However, regarding part (b), I'm in trouble. Intuitively, I'd imagine to aim a bit higher uphill and downhill, just like on a horizontal plane. But, according to the book, I'm wrong: I need to aim lower! Why!?

Answer

This is probably not a question which can be answered intuitively.

When shooting uphill the component of gravity normal to the incline is reduced, so for a given time of flight the bullet will fall less. However, there is now a component of gravity down the plane, which increases the time of flight. Whether these 2 effects compensate exactly, or which one dominates, is not obvious.

As DLM suggests, do the calculation again and compare the 2 scenarios.

In the extreme case of shooting directly above you (in an anticlockwise sense), the barrel will be aiming "high" (further anti-clockwise) so you would need to aim "low" (clockwise). However, we cannot presume this applies at all angles below 90 degrees, because it may channge over at some point.